This proposal is the first revision of the 4th competitive renewal of a project that brings together an international team of investigators. The specific goals include: 1 .To continue our investigation into the analysis of survival data. Of interest is the study of alternatives to the proportional hazards model. We plan to investigate measures of explained variation both in the survival and competing risks framework. We also plan to study problems that arise in observational databases such as the use of propensity scores in hypothesis testing and the efficiency of matched pairs versus cohort analysis. 2. To continue our investigation into methods for multistate and multivariate survival analysis. We plan to continue our development of techniques for direct modeling and inference for the probability a subject will be in a given state given covariates. Of particular interest are techniques developed using an inverse probability weighting technique or using a pseudo-value regression formulation. We plan to develop data specific models for HOST outcomes and software that can be used interactively by patients and clinicians to decide transplant treatment options and models for the development of acute graft-versus-host disease. We will examine models for the graft-versus-leukemia effect in HSCT by looking at how intermediate events modulate response or by dividing covariate effects into direct and indirect effects based on an intermediate event. We will continue our study of frailty models by development of a model with an increasing association over time and inference for models where the frailty model depends on the covariates. Finally, we will study frailty models when the data are sampled in a case cohort study. 3.To continue are study of statistical techniques for longitudinal studies by examining problems specific to clinical trials. Problems to be investigated include the study of techniques for trials with an adaptive treatment strategy, techniques for sequential monitoring of trials with long term outcomes as a primary goal but crossing hazards and methods for the design and analysis of trials with competing risks as an outcome. 4. To continue our efforts in transferring this technology from the statistical literature to the medical literature and common practice in data analysis. This involves writing expository articles for the medical literature, the development of user-friendly software and presentations to medical investigators.